The field of the invention is systems and methods for magnetic resonance imaging (“MRI”). More particularly, the invention relates to systems and methods for preserving phase information in diffusion-weighted MRI, including diffusion tensor imaging (“DTI”), diffusion spectrum imaging (“DSI”), q-ball imaging (“QBI”), and the like.
Diffusion-weighted MRI (“dMRI”) is a useful too for providing valuable neuroscientific and clinical information. In dMRI, magnetic resonance signals are sensitized to anisotropic water diffusion through localized signal attenuation. Diffusion MRI models, such as DTI, DSI, and QBI can use this diffusion weighting dependent signal attenuation to obtain structural tissue information.
A magnetic resonance signal is complex-valued and, therefore, includes both magnitude and phase components. During the diffusion encoding process, which is realized by applying magnetic field gradients in specific directions, physiological and other motion sources can cause smooth phase variations across the acquired complex image. Examples of such physiological motion sources includes brain motion, cardiac motion, and respiratory motion.
These background phase variations do not have an impact on the magnitude of the image; thus, diffusion MRI commonly uses magnitude-only images, which are insensitive to these background phase variations. A drawback of using magnitude-only images arises, however, when multiple such images are combined in some way. For example, if the multiple images are combined (e.g., added) and used for model fitting or signal averaging, the magnitude noise tends to accumulate in a way that zero-mean noise (where half the fluctuations are positive and half are negative) does not. This accumulation of noise is generally not an issue if the signal-to-noise ratio (“SNR”) of the acquired image is high because the distribution of noise approximates a Gaussian distribution in such cases. In diffusion-weighted MRI and other low SNR modalities, however, signal averaging can accumulate non-Gaussian noise, which results in biased data points at low signal intensities.
Thus, in these low signal-to-noise ratio (“SNR”) cases, where many low SNR images are combined, there is a severe penalty to combining magnitude images compared to complex images. This is exactly the regime in which diffusion MRI analysis is situated. Namely, hundreds of low-SNR magnitude images are typically acquired with different diffusion directions, after which these images are used as the source to various computed images. As a result, diffusion modeling of signal gets less accurate in low SNR regions because noise has a strong influence on signal attenuation. This influence of the noise leads to incorrect or biased model fits.
Combining low SNR magnitude images in an attempt to improve SNR, such as by using signal averaging, is also problematic because the signal averaging assumes a Gaussian noise distribution with a zero mean. But, noise in magnitude data follows a non-central chi-square distribution with a non-zero mean. As a result, the signal averaging leads to a strong influence of noise and an artifact in terms of signal bias, yielding low contrast in averaged images. For complex-valued signals, averaging is only a valid concept if carried out in the complex domain, which is not directly possible because background phase contamination destroys signal coherence of the phase.
A recent attempt at reducing the background phase contamination in diffusion-weighted MRI was discussed by S. J. Holdsworth, et al., in “Diffusion tensor imaging (DTI) with retrospective motion correction for large-scale pediatric imaging,” J. Magn. Reson. Imaging, 2012; 36:961-971. In this approach, the acquired k-space data is apodized using a triangular window filter having a fixed size (e.g., 25 percent of k-space). Because this approach removes the higher spatial frequencies in k-space, spatial resolution in the resultant images is reduced. This reduction in spatial resolution can result in missing fast-changing phase variations, such as those that typically occur at tissue borders or where significant subject motion results in rapid phase changes. As a consequence, these fast phase variations may not be estimated or otherwise removed. Another drawback of this method is that stronger diffusion weightings (i.e., higher b-values) result in more phase variations, which also might not be estimated or otherwise removed based on the apodization of k-space.
Another attempt at reducing the background phase contamination in diffusion-weighted MRI was proposed by J. I. Sperl, et al., in “Phase Sensitive Reconstruction in Diffusion Spectrum Imaging Enabling Velocity Encoding and Unbiased Noise Distribution,” In Proceedings of the 21st annual meeting of ISMRM, Salt Lake City, 2013; p. 2054. This approach utilized a low-order polynomial fitting and subtraction of the image phase across image space, and a linear fitting and subtraction of the phase evolution across diffusion space (i.e., “q-space”). The low-order polynomial fitting used in this approach may be valid for low b-values, but it is not a reliable approach when larger b-values are used because with higher b-values, background phase contamination becomes increasingly complicated and therefore harder to fit with a low-order polynomial term. The polynomial fitting is also not as reliable at resolving phase jumps at tissue borders. Another drawback with this method is that a large range of q-space has to be covered (i.e., multiple diffusion directions and weightings need to be acquired).
After removing the polynomial phase term in image space, a linear term across the different b-values (i.e., in q-space) is estimated using a linear fitting. This two-step approach removes the linear term after the background phase is removed in the first step. There is reason to believe, however, that the polynomial phase term and the linear phase term are not independent of each other; thus, a two-step approach of estimating and removing these effects is likely to introduce errors in the final reconstruction.
In light of the foregoing, there remains a need to provide a reconstruction algorithm for diffusion-weighted MRI that is capable of reliably estimating and removing undesired background phase variations, such that complex-valued data can be utilized in diffusion analyses, such as diffusion tensor calculations and tractography methods.